A homogenous product is produced by two rival firms. They have the same costs. P = 80 – Q P = 80 – Q1 - Q2 The market demand is: or The firms' total cost equations are: TC1 = 50Q1 TC1 = 50Q1 Both firms choose their output level at the same time. In estimating its marginal revenue, each firm takes its rival's price as given and maximizes profit subject to that assumption. Each firm is thus a price-taker, and behaves like a firm in perfect competition: Marginal revenue equals price under its assumption, so Firm 1 sets price equal to marginal cost. Use this fact to derive Firm 1's reaction equation. а. Q1*(Q?) %3D b. In the Bertrand duopoly equilibrium, each firm charges the same price (the product being homogeneous). Can we solve for the equilibrium output of each firm? c. Find the total combined output, revenue, cost, and profit: TR = TC = П

A homogenous product is produced by two rival firms. They have the same costs. P = 80 – Q P = 80 – Q1 - Q2 The market demand is: or The firms' total cost equations are: TC1 = 50Q1 TC1 = 50Q1 Both firms choose their output level at the same time. In estimating its marginal revenue, each firm takes its rival's price as given and maximizes profit subject to that assumption. Each firm is thus a price-taker, and behaves like a firm in perfect competition: Marginal revenue equals price under its assumption, so Firm 1 sets price equal to marginal cost. Use this fact to derive Firm 1's reaction equation. а. Q1*(Q?) %3D b. In the Bertrand duopoly equilibrium, each firm charges the same price (the product being homogeneous). Can we solve for the equilibrium output of each firm? c. Find the total combined output, revenue, cost, and profit: TR = TC = П

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

Somehow Im having trouble with parts a-c. Could I have help understanding and solving giving this is a Bertrand duopoly model.

A homogenous product is produced by two rival firms. They have the same costs.
P = 80 – Q
P = 80 – Q1 – Q2
The market demand is:
or
The firms' total cost equations are:
TC1 = 50Q1
TC1 = 50Q1
Both firms choose their output level at the same time. In estimating its marginal revenue,
each firm takes its rival's price as given and maximizes profit subject to that assumption.
Each firm is thus a price-taker, and behaves like a firm in perfect competition: Marginal
revenue equals price under its assumption, so Firm 1 sets price equal to marginal cost. Use
this fact to derive Firm 1's reaction equation.
а.
Qi*(Q?) :
b. In the Bertrand duopoly equilibrium, each firm charges the same price (the product being
homogeneous). Can we solve for the equilibrium output of each firm?
c. Find the total combined output, revenue, cost, and profit:
Q
TR =
TC

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